• Get your .BMP file of the sprite you want
• Open CD Mage
• Open the FFT ISO
• Go to the Battle Folder
• Extract all the .SPR files or just the one you want. I found it a less of a hassle in the long run to extract them all incase you wanted more new sprites later
• Open Shishi Sprite Editor
• Open the .SPR file you want to overwrite
• File -> Import: .BMP Image of the new Sprite
• File -> Save
• Import the saved .SPR into the battle folder
• Start FFT!

For a full listing of Sprites and their related file names, visit here.